The ordinary two-dimensional (2D) game of tic-tac-toe (TTT), having 3.times.3 cells, is well known. It is suitable for play by children, but there are relatively few strategies, and most players with experience achieve the theoretically-predicted draw.
TTT has been implemented in three dimensions (3D) by vertical stacking of boards, each of 3.times.3 or 4.times.4 cells, and respectively 3 or 4 high. The 3.times.3.times.3 version is a trivial win for the first player to move in a two-player game (two-player games are assumed herein unless otherwise stated.) The more complex 4.times.4.times.4 3-D game has been predicted to be a win for the first player, although the strategy is less directly obvious from the 2D 3.times.3 game than is the strategy for the 3.times.3.times.3. Vertically stacked games in both formats have been sold from time to time, but have not been commercially successful on a continuing basis. This may be because they are physically complex, taking up space and being prone to breakage; or because they are not satisfyingly complex in terms of strategy. In either case, no following has developed (compare Monopoly.RTM.--or even Othello.TM.).
There do not appear to be examples of the proposed board structure or layout in the art, and in particular in U.S. Class 273/271 ("Tic-Tac-Toe games"). Compton (U.S. 4,371,169) proposed "imaginary multilevel tic-tac-toe". In FIG. 7 of Compton, a 1-dimensional array of 3.times.3 boards is shown; in FIG. 9, a crossed arrangement of 3.times.3 boards is illustrated; and in FIG. 2A, the 3.times.3 boards are arranged circularly. Boyer et al (U.S. 4,131,282) illustrate a 3.times.3 array of tiles each tile having a 3.times.3 array of cells (a "3.times.3:3.times.3" array), and propose a n.times.n:n.times.n array where n is an integer. However, the proposed rules of play in Boyer et al involve a multiplicity of colors and do not correspond to classical TTT, or to the rules proposed here.